In this paper, we have discussed the application of the hopping parameter expansion to the reweighting factor Eq. (REF )
for quenched QCD configurations.
Besides the truncation error of the hopping parameter expansion,
applicability range of the method is limited also by the overlapping problem of the reweighting method [1]}, [2]}, [3]} .
Here, we note that the effective theory we developed is applicable also to generate configurations
effectively incorporating dynamical quark effect up to \(n_{\rm max}\) -th order of the hopping parameter expansion:
\(S_{\rm eff} = -2N_c N_{\rm site} \, \beta ^* \hat{P} - N_s^3 \lambda \, {\rm Re} \hat{\Omega }\quad \textrm {with} \;\; \lambda = N_{\rm f} N_t \, L^0 (N_t, N_t) \, (\kappa ^*)^{N_t},\) 
